The effect of quantum probability on the world
I'm going to take this as a thought experiment to the effect of: How much does non-determinism at the quantum level affect predictability at human scale?
The lightning strike
Imagine we return to before the lightning strike, and assume that we essentially rerun time from then, how different could or would it look from History 1?
The path of the lightning itself, and the place where it strikes, is set up (as far as I'm aware) by the distribution of temperatures and ions between the heavily charged cloud and the ground. So if we return to the very instant before the lightning strike, I would expect that strike to happen in exactly the same place; a lightning strike is a big thing set up by millions of ions.
If we step back a few seconds, then the picture is much less clear; we do not yet know exactly what triggers a lightning strike - the potential difference is not enough for a spontaneous spark. One possible trigger is cosmic ray showers creating an initial ionised path which then begins a cascade of electrons which amplify the ionisation and ultimately (sometimes) permit an arc. Would such a cosmic ray shower happen in the same way twice? Well, probably. The cosmic ray particle was already heading towards the Earth, though it is hard to make judgements about the determinism of its point of impact on the atmosphere; under the Copenhagen interpretation, we cannot talk about whether the particle was on a particular path beforehand.
Returning to a day or more before the strike I would intuitively say we are into the realms of the strike being unlikely to happen in the same place at the same time. The very actions of other lightning flashes (which are themselves unpredictable) within the storm structure will change the distribution of ions in and near the cloud. Even if the same cosmic ray particle induces a similar shower, the chances that it would invoke the same effect seem low.
A lot of the determinism that such a story relies on would largely work; people are large macroscopic beings driven by the actions of large macroscopic events, so really they are largely deterministic on short time scales.
However, even if people do largely the same things, the relative timing of those things may not be so deterministic; automobile incidents, lottery draws, even fertilisation are all sensitive to precise timing.
We intuitively understand this from our experience of life; chance meetings which would not have happened, chance tragedies, and so on. Nondeterminism even with such a small immediate effect leads to large differences even weeks or months later, let alone years.
There is a slightly alarming lack of time-asymmetry in quantum physics. Things look largely the same backwards as forwards. Feynman diagrams codify this; an antiparticle is represented as a particle moving backward in time. Really all we have to tell us about the past are artefacts and memories which exist in the present; so the idea of going backward in time could be considered analogous to going forward into the future; it may be as indeterminate in either direction. Thus, it could be argued that you would only go back to one of many possible histories. From there, evolving time forward again would be extraordinarily unlikely to evolve to the same future, and you can wave goodbye to going back to the past again a second time.
This classic thought experiment was intended to highlight the oddness of connecting the macroscopic world directly to the quantum. It is not a reflection of reality, though; the mechanism which kills the cat is one that connects a macroscopic object to a quantum process, which is already set up to cause decoherence; the particle may be in a superposed state, but as soon as the vial is affected, the superposition has decayed and the cat is on one path or the other. We are still in the process of understanding the mechanisms and implications of the process of decoherence of a quantum state, particularly as we reach for tools to manipulate it in quantum computation.